The gas mileage for a particular model car is known to have a standard deviation of σ = 1.0 mile per gallon in repeated tests in a controlled laboratory environment at a fixed speed. For a fixed speed, gas mileages in repeated tests are Normally distributed. Tests on three cars of this model at 65 miles per hour give gas mileages of 24.3, 24.9, and 24.8 miles per gallon. What is the z statistic for testing H0: μ = 25miles per gallon based on these three measurements? (Round your answer to three decimal places.)

z=

z = -0.577

Step-by-step explanation:

sample mean = ( 24.3 + 24.9 + 24.8 ) / 3 = 24.667

n = 3

σ = 1.0

Test statistic:

z = ( 24.667 - 25 ) / ( 1/SQRT(3) )

z = -0.577

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

∠cbe and ∠deb are same-side interior angles.

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